Combine all dry ingredients together in a large bowl. Add all remaining ingredients and stir until well combined. Pour into un-greased 9×13 inch baking pan and bake for 50 minutes or until tester inserted in center of cake comes out clean. Cool.

My bad! But yes, I do think coconut flour would work just fine here since there is so much moisture going on. I would start out with just 1 cup of it, bump the eggs up to 5 (a safe rule for coconut flour is five eggs to a cup) and add some water or milk if need be.
Or, you could take a look at this recipe: http://www.freecoconutrecipes.com/index.cfm/2008/5/4/Carrot-Cake-with-Coconut-Flour

Can I use all coconut flour here instead of wheat and coconut? There seems to be plenty of eggs and oil to add the requisite moisture the coconut flour needs, but Im not sure. We try and avoid grains, but still long for an excellent carrot cake recipe!! Any advise anyone? Sarah, perhaps you can help me with this one? xoxo

Here is the Stevia substitution i use in baking.
1tsp stevia(powdered)=1 cup sugar
1tsp stevia(liquid)=1 cup sugar
Then for every 1 cup sugar replace by stevia, add 1/4 to 1/2 cup of either:
applesauce, fruit puree, fruit juice, yogurt or any other thing that will work well with your recipe and give it the required moisture. happy baking.

If you can’t handle sugar like me, then you should as well avoid honey because they will both spike up blood sugar. Stevia is very good in baking, just be sure to substitute with some liquid or apple sauce to compensate for the volume you will loose by not using sugar. I will come back to give you the correct substitution soon. Stevia is my favourite sweetner.

Sara: The coconut cream icing will for sure separate if left out by itself. If it’s on the cake however, it shouldn’t be a problem. And yes, please refrigerate the cake if it’s going to sit overnight. If you want to eat it at room temp just let it sit out for an hour or so before serving. Hope you enjoy! :)

This cake is the BOMB!!!! NO JOKE. I didn’t use the coconut flour cause I didn’t have any. I used Whole Wheat Pastry Flour instead. I only used 1 tbsp of baking powder and 1 tbsp of baking soda. I used the Cream Cheese Icing receipe and it was wonderful. Thank you so much for this receipe.

I don’t know about stevia, you probably can but it won’t be the same. Applesauce won’t work. Just cut back on the sugar (or omit it, it’s only 1/4 cup) and reduce the honey. This is a cake though, and a pretty large one at that. So the sugar amount is actually pretty reasonable. But feel free to play with the sugar and honey amounts to your taste.